On Crystallography, 457 



stals should indicate the angles which their faccg m;ike 

 with each other. Such are the indications which niake the 

 dcscri|)Uou Start up, as it were, hy palpable and truly cha- 

 racteribtic traces. Without these requisites, a de^eription 

 would be a rude and imperfect sketch, which nnght be re- 

 iern d to many diiferent ol)ject8. 



'rhus v/e do not describe dodee.ihedral zircon v\ hen we 

 merely sav that it is a prism with lour panes ternimated by 

 summits with four rhombs which arise on the longiiudinal 

 ridires. This character would also suit the harmotome 

 '(the cruciform hyacinth), the htilbile, oxidized tin, i^cc. : 

 but if you add that the panes form right angles with each 

 other, and the fares of the summit are inclined to taclf 

 other by 124° 12% the description will be restrained to 

 zircon. If you say that the inclination is 121" b^\ it will 

 be the harmotome ; or, if you say that there are two dif- 

 ferent inclinations, the one 123'' 32\and the other 112* 

 14% it will be the siiibite. 



There are several varieties of one and the same substance 

 which may present forms of the same kind, and wh.ch will 

 only be distinguished by the measurements of their angles. 

 Of this description are the six rhomboids on one hand, 

 and on the other the two dodecahedrons with rhombib 

 faces which are found in carbonated lime. How can we 

 exactly describe all the varieties which differ froui each 

 other more or less, if we do not precisely mark the dif- 

 fereiKt s ? And there are even cases in which the use of 

 the gomometer is the only vva\ to avoid an error which 

 would not -fair to slide into the description. -Thus the 

 calcareous rhon^^boid, the angles of- which only differ ia 

 about 2 : 18' from the right angle, w^as at first taken for 

 a cube, and wouhl have continued to be called cubical 

 calcareous spar, if geometrical measuremenis had not rec- 

 titied ihis denonhnarion, doubly deieciive, either in itself,' 

 or with relLienee to the theory which demonstrates tiiat 

 the existence of" the cube does not agree here with that 

 of any symmetrical laws (if decrc^mtnt. 



One of the principal cau>es of this neglect o? gonio- 

 metry arises from the kind of rule to w-hkCh some mmera- 

 Jogisis are restricted, of con lining tlicmselves to cnaracters 

 susceptible of being dttermineci solely by a refercrce to the 

 senses : and .on this account we are deprived of the re- 

 sources presented by the instrumeiits \'. hich g.ve to our 

 organs a new degree of d iicacy, and render them capable 

 of attaining, in the dctennniation of the distmguishing 

 characters of minerals^ that precision which is in its turn 



tne 



